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5.26.9  Choosing the GCD algorithm of two polynomials : ezgcd heugcd modgcd psrgcd

ezgcd heugcd modgcd psrgcd denote the gcd (greatest common divisor) of two univariate or multivariate polynomials with coefficients in ℤ or ℤ[i] using a specific algorithm :

Input :

ezgcd(x^2-2*x*y+y^2-1,x-y)

or :

heugcd(x^2-2*x*y+y^2-1,x-y)

or :

modgcd(x^2-2*x*y+y^2-1,x-y)

or :

psrgcd(x^2-2*x*y+y^2-1,x-y)

Output :

1

Input :

ezgcd((x+y-1)*(x+y+1),(x+y+1)^2)

or :

heugcd((x+y-1)*(x+y+1),(x+y+1)^2)

or :

modgcd((x+y-1)*(x+y+1),(x+y+1)^2)

Output :

x+y+1

Input :

psrgcd((x+y-1)*(x+y+1),(x+y+1)^2)

Output :

-x-y-1

Input :

ezgcd((x+1)^4-y^4,(x+1-y)^2)

Output :

"GCD not successful Error: Bad Argument Value"

But input :

heugcd((x+1)^4-y^4,(x+1-y)^2)

or :

modgcd((x+1)^4-y^4,(x+1-y)^2)

or :

psrgcd((x+1)^4-y^4,(x+1-y)^2)

Output :

x-y+1

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